In conventional electrically pumped surface-emitting semiconductor laser components, owing to the usually low conductivity of the semiconductor materials of the semiconductor body in a lateral direction, the pump current is often injected into the semiconductor body from the n-conducting side thereof via a current spreading layer. By way of example, layers made of III-V semiconductor materials, such as n-GaAs, are used for this purpose. However, current spreading layers of this type frequently likewise have a low conductivity in a lateral direction, said conductivity often being comparable to that of the semiconductor body, or absorb the radiation generated in the active zone. On account of the low conductivity, a current spreading layer of this type, for efficient current injection, often has to be embodied with a large thickness, as a result of which the radiation power absorbed in the current spreading layer is increased, however. Overall, the risk of a reduction of the efficiency of the semiconductor laser component is increased on account of the low conductivity in a lateral direction and/or the absorption.